Meanwhile, Arsenal manager Unai Emery is under tremendous pressure in order to save his job after a poor start to the season with his side just three points clear of Spurs and eight away from the top four.
And Redknapp believes Arsenal would be right to consider Pochettino, adding that the fans would accept anybody as long as the club were winning games.
"With Pochettino going from Tottenham, there will be one or two Premier League managers waking up this morning thinking, ‘oh my God, this ain’t too clever’,” he told talkSPORT.
He continued, "And there will be one or two chairmen very excited this morning thinking if there’s any way they could get him in. What a signing he’d be."
Revealing Arsenal as a decent choice for Pochettino, Redknapp stated, "There are clubs in London who are having a terrible time. Why shouldn’t he go to Arsenal if he wants to? You think the Arsenal fans wouldn’t love him there?"
Handing in famous dictator Saddam Hussein's analogy, the former Spurs manager said, "If you go in there and start winning football matches, they would have taken Saddam Hussein in there when he was about, the fans don’t give a monkey's! If you start winning every week, they’re singing ‘there’s only one Saddam’."
He concluded, "It happens in football – Sol Campbell went from Tottenham to Arsenal, George Graham did it, Terry Neill did it, Pat Jennings, one of our greatest goalkeepers in history, even he made the change. It can happen, as long as you can do the job. I would have thought Arsenal will be looking at Pochettino now thinking, ‘could we? Can we?’"